Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium,
2019
Shri Ramswaroop Memorial University
Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _
Applications and Applied Mathematics: An International Journal (AAM)
One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.
Spectral Tau-Jacobi Algorithm For Space Fractional Advection-Dispersion Problem,
2019
Helwan University
Spectral Tau-Jacobi Algorithm For Space Fractional Advection-Dispersion Problem, Amany S. Mohamed, Mahmoud M. Mokhtar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we use the shifted Jacobi polynomials to approximate the solution of the space fractional advection-dispersion. The method is based on the Jacobi operational matrices of fractional derivative and integration. A double shifted Jacobi expansion is used as an approximating polynomial. We apply this method to solve linear and nonlinear term FDEs by using initial and boundary conditions.
On Nonlinear Contractions In New Extended 𝒃-Metric Spaces,
2019
Université de Sousse
On Nonlinear Contractions In New Extended 𝒃-Metric Spaces, Hassen Aydi, Abdelbasset Felhi, Tayyab Kamran, Erdal Karapınar, Muhammad U. Ali
Applications and Applied Mathematics: An International Journal (AAM)
Very recently, the notion of extended 𝑏-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended 𝑏-metric space is given.
Summation Formulas For The Confluent Hypergeometric Function , Φ_ 2^(2r) Of Several Variables,
2019
Aden University
Summation Formulas For The Confluent Hypergeometric Function , Φ_ 2^(2r) Of Several Variables, Ahmed A. Atash
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we establish a general summation formula for the confluent hypergeometric function Φ2(2r) of several variables by applying the generalized Kummer’s summation theorem due to Lavoie et al. As an applications of our main result, we obtain certain new summation formulas for the confluent hypergeometric function Φ24 . Also some summation and transformation formulas including a results obtained recently by Choi and Rathie have been obtained as special cases.
Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle,
2019
California State University, San Bernardino
Pascal's Triangle, Pascal's Pyramid, And The Trinomial Triangle, Antonio Saucedo Jr.
Electronic Theses, Projects, and Dissertations
Many properties have been found hidden in Pascal's triangle. In this paper, we will present several known properties in Pascal's triangle as well as the properties that lift to different extensions of the triangle, namely Pascal's pyramid and the trinomial triangle. We will tailor our interest towards Fermat numbers and the hockey stick property. We will also show the importance of the hockey stick properties by using them to prove a property in the trinomial triangle.
The Martingale Approach To Financial Mathematics,
2019
California Polytechnic State University, San Luis Obispo
The Martingale Approach To Financial Mathematics, Jordan M. Rowley
Master's Theses
In this thesis, we will develop the fundamental properties of financial mathematics, with a focus on establishing meaningful connections between martingale theory, stochastic calculus, and measure-theoretic probability. We first consider a simple binomial model in discrete time, and assume the impossibility of earning a riskless profit, known as arbitrage. Under this no-arbitrage assumption alone, we stumble upon a strange new probability measure Q, according to which every risky asset is expected to grow as though it were a bond. As it turns out, this measure Q also gives the arbitrage-free pricing formula for every asset on our market. In …
Rare Event Sampling In Applied Stochastic Dynamical Systems,
2019
New Jersey Institute of Technology
Rare Event Sampling In Applied Stochastic Dynamical Systems, Yiming Yu
Dissertations
Predicting rare events is a challenging problem in many complex systems arising in physics, chemistry, biology, and materials science. Simulating rare events is often prohibitive in such systems due to their high dimensionality and the numerical cost of their simulation, yet analytical expressions for rare event probabilities are usually not available. This dissertation tackles the problem of approximation of the probability of rare catastrophic events in optical communication systems and spin-torque magnetic nanodevices. With the application of the geometric minimum action method, the probability of pulse position shifts or other parameter changes in a model of an actively mode-locked laser …
Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship,
2019
Taylor University
Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton
ACMS Conference Proceedings 2019
Part of the goal of discipleship at the Christian university is for faith development to seep into the hearts of the students. Similarly, the goal of the development of future mathematicians is for the mathematical proficiencies, the practices like problem solving and analytical reasoning that permeate each of the courses, to seep into the hearts of our majors. This presentation shares how the weaving of our spiritual and disciplinary discipleship efforts benefits the faith development of our students while also helping them to think like a mathematician.
From Perfect Shuffles To Landau's Function,
2019
Presbyterian College
From Perfect Shuffles To Landau's Function, Brian D. Beasley
ACMS Conference Proceedings 2019
If we view a given shuffle of a deck of cards as a permutation, then repeatedly applying this same shuffle will eventually return the deck to its original order. In general, how many steps will that take? What happens in the case of so-called perfect shuffles? What type of shuffle will require the greatest number of applications before restoring the original deck? This talk will address those questions and provide a brief history of the work of Edmund Landau on the maximal order of a permutation in the symmetric group on n objects. It will also note some recent progress …
Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses,
2019
California State University
Replacing Remedial Mathematics With Corequisites In General Education Mathematics Courses, Alana Unfried
ACMS Conference Proceedings 2019
Many colleges and universities offer courses, such as Remedial Mathematics or Elementary Algebra, that underprepared students must complete before they can take a college-level mathematics course. However, nationally there is a push to replace remedial mathematics courses with corequisite courses instead. This design allows students to enter directly into their general education mathematics course instead of first overcoming the barrier of a remedial course. Corequisite mathematics courses were implemented across the 23-campus California State University system during the 2018-19 academic year. I will discuss the design and implementation of a corequisite structure at California State University, Monterey Bay, in particular …
Charles Babbage And Mathematical Aspects Of The Miraculous,
2019
Anderson University
Charles Babbage And Mathematical Aspects Of The Miraculous, Courtney K. Taylor
ACMS Conference Proceedings 2019
Charles Babbage is widely known as the father of the computer, but he is lesser known for his contributions to natural theology and apologetics. In 1837 Babbage wrote the Ninth Bridgewater Treatise in response to a series of writings concerning faith and science that had been commissioned by the Royal Society. Among the remarkable features of the Ninth Bridgewater are mathematical analogies concerning the miraculous. We will explore these ideas, which range from the difference engine to a family of fourth degree curves, illustrating that for Babbage, miracles are not exceptions to natural law, but rather instances of a larger …
The Applicability Of Mathematics And The Naturalist Die,
2019
California Baptist University
The Applicability Of Mathematics And The Naturalist Die, Ricardo J. Cordero-Soto
ACMS Conference Proceedings 2019
Philosopher and Christian apologist William Lane Craig has proposed a valid deductive argument for God’s existence that is rooted in the applicability of mathematics to the physical universe. This argument was presented by Craig during a debate with philosopher and atheist Alex Rosenberg. During the debate, Rosenberg presented a rebuttal to the soundness of this argument by appealing to chance as an explanation to the applicability of mathematics to the physical universe. In this talk, the presenter will discuss how the naturalist die is unable to produce “chance application” of mathematics while defending the soundness of the argument in light …
Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth,
2019
Indiana Wesleyan University
Faith, Mathematics, And Science: The Priority Of Scripture In The Pursuit And Acquisition Of Truth, Bob Mallison
ACMS Conference Proceedings 2019
This research will examine some approaches for identifying truth as well as some issues involved in recognizing reliable sources of information. We will proceed from a decidedly Christian perspective including the conviction that God created an orderly universe (and that studying nature provides valuable information about Him) and that His Word, the Bible, even more clearly expresses in- formation about Him. We will discuss some of the essential tools used by mathematicians and scientists for the discovery of truth – namely, models. We will examine some valuable models from history, and briefly discuss that as additional scientific information became available, …
Teaching Mathematics At An African University -- My Experience,
2019
University of the Gambia
Teaching Mathematics At An African University -- My Experience, Kathleen Lewis
ACMS Conference Proceedings 2019
For eight years (2010-2018), I was the head of the math department at The University of The Gambia, a small, new (started in 1999) university in a very small, mostly Muslim, West African country that most Americans have never heard of. During that time, a number of other Americans and Europeans came to teach for shorter periods of time. I will talk about what this experience was like for us, both the good and the bad. I will describe the possibilities for others to spend either a sabbatical or an extended period of time at such a university and suggest …
Lagrange's Interpolation, Chinese Remainder, And Linear Equations,
2019
Point Loma Nazarene University
Lagrange's Interpolation, Chinese Remainder, And Linear Equations, Jesús Jiménez
ACMS Conference Proceedings 2019
Consider a finite set of points {(x1, y1), (x2, y2), . . . , (xk , yk )} in R2. The Lagrange’s interpolation problem is to find a polynomial p(x) of degree k − 1 satisfying p(xi) = yi for 1 ≤ i ≤ k. We will recall the solution to Lagrange’s interpolation problems as an instance of the Chinese Remainder Theorem. Next, we will show that a similar approach can be used to construct solutions to a system of linear equations.
Addressing Challenges In Creating Math Presentations,
2019
Liberty University
Addressing Challenges In Creating Math Presentations, David Schweitzer
ACMS Conference Proceedings 2019
When it comes to composing presentation slides with extensive mathematical content, each of the slide creation platforms has at least one significant drawback. Whether it is Beamer and its steep learning curve, PowerPoint and its relative inefficiency with math, Google Slides and its complete lack of math capabilities, or some other platform, no one tool single-handedly offers an ideal solution. Additionally, if users desire creative flexibility, such as the ability to easily change fonts or colors, the platforms’ respective limitations can become even more pronounced. In a project that has been well suited for undergraduate research, the presenter and his …
Overcoming Stereotypes Through A Liberal Arts Math Course,
2019
Winthrop University
Overcoming Stereotypes Through A Liberal Arts Math Course, Jessica Hamm
ACMS Conference Proceedings 2019
"I'm just not a math person.” We’ve heard this comment countless times from our students. It is a mentality that both paralyzes and strangely comforts them. In this talk I will describe how I use my liberal arts Joy of Mathematics course to help students address and overcome stereotypes. In particular, I will discuss a specific assignment as well as share some student comments and perspectives on how this course helped change their viewpoint on more than just math.
Maximum Elements Of Ordered Sets And Anselm's Ontological Argument,
2019
Miami University
Maximum Elements Of Ordered Sets And Anselm's Ontological Argument, Doug Ward
ACMS Conference Proceedings 2019
I will present a simple theorem concerning maximal elements of a set T endowed with an ordering “>” that is antisymmetric, i.e., if A and B are elements of T , we cannot have both A > B and B > A. A special case of this theorem is a simple version of the ontological argument, one of the classical proofs for the existence of God.
Numerical Range Of Toeplitz Matrices Over Finite Fields,
2019
Taylor University
Numerical Range Of Toeplitz Matrices Over Finite Fields, Derek Thompson, Maddison Guillaume Baker, Amish Mishra
ACMS Conference Proceedings 2019
We characterize the kth numerical range of all n×n Toeplitz matrices with a constant main diagonal and another single, non-zero diagonal, where the matrices are over the field Zp[i], with p a prime congruent to 3 mod 4. We find that, for k ∈ Z∗, the kth numerical range is always equal to Zp[i] with the exception of the scaled identity. We also use similar techniques to discover a general connection between the 0th numerical range and the kth numerical range. Lastly, we conclude with a conjecture regarding the general numerical range of all triangular Toeplitz matrices.
Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner,
2019
Gordon College
Is Mathematical Truth Time Dependent? Comments From A Paper By Judith Grabiner, Richard Stout
ACMS Conference Proceedings 2019
Judith Grabiner, a renowned historian of mathematics, has written many papers related to signifi- cant changes in the content and nature of analysis, from the 17th through the 19th century. In her paper “Is Mathematical Truth Time Dependent?” Professor Grabiner gives several reasons for the changing nature and requirements in rigor that occurred over this period of two hundred years. In this talk I will briefly summarize her conclusions, particularly in light of how they might influence a Christian perspective on mathematics.
